Averages — mean, median, mode and range — appear in nearly every 11+ maths paper. Children who don't know which is which lose easy marks; children who do can score 5-10 marks here without much thought.
The four definitions
- Mean — the total of all values divided by how many values there are. (5+7+9)÷3 = 7.
- Median — the middle value when the numbers are arranged in order.
- Mode — the most frequent value. Can be more than one (bimodal) or none.
- Range — the highest value minus the lowest value.
Worked examples
Find all four for: 4, 7, 2, 7, 9
- Sort first: 2, 4, 7, 7, 9
- Mean: (2+4+7+7+9) ÷ 5 = 29 ÷ 5 = 5.8
- Median: middle value = 7
- Mode: 7 (appears twice)
- Range: 9 - 2 = 7
11+ trickier questions
Common harder twists:
- "The mean of 5 numbers is 12. Four of the numbers are 10, 11, 13, 15. Find the fifth." Total must be 60. 10+11+13+15 = 49. So fifth = 11.
- "What number could be added to 3, 7, 4 to make the mean 5?" Total of three = 14. Need total of 20 for mean 5 over 4 numbers. Answer: 6.
- Median of an even number of values: take the average of the two middle values.
Common errors
- Forgetting to sort before finding median.
- Confusing mode and median.
- Not including all values in the mean calculation.
Quest Arena's maths worksheets include 25 averages drill sheets.